Determining reserves of a reservoir

ABSTRACT

This disclosure provides embodiments of computer implemented methods, computing apparatuses, and other methods for determining reserves of a reservoir. For example, an embodiment of the computer implemented method includes receiving field data for a field that comprises a reservoir, wherein the field data includes pressure data and cumulative production data. The embodiment further includes generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data. The embodiment further includes generating a normalized pressure graph, wherein the normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from U.S. Provisional Patent Application No. 61/909,406, filed on Nov. 27, 2013, atty. docket no. T-9400-P, the disclosure of which is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates generally to reservoir management, and more particularly to linear flow, boundaries, and determining reserves of a reservoir.

BACKGROUND

Field operations (e.g., exploration procedures) are used to capture and retrieve one or more resources from a reservoir of a subterranean formation. Knowing the amount of these resources (also called reserves) in the subterranean formation can help a company to determine whether a field operation should be performed and, if so, what that field operation should be.

For resources that are fluid (not a solid), the flow rate and pressure variation with time can be used to calculate the volume of the subterranean resource. However, calculating the volume of the subterranean resource is generally only possible when pressure and production records are long enough so that the boundaries of the reservoir control flow rate and pressure behavior in what is called boundary dominated flow.

When the reservoir has low permeability, the low permeability makes the time to reach boundary dominated flow extremely large (sometimes years). Until that time, the reservoir is in a transient condition, making estimation of the amount of the subterranean resource difficult to determine with certainty. Hydraulic fracturing is sometimes utilized to create artificial fractures in an effort to increase permeability and induce the subterranean resource to flow to a wellbore, but the low permeability still dominates drainage behavior and makes estimation of the amount of the subterranean resource difficult.

To try to estimate the amount of the subterranean resource inside the region stimulated by the hydraulic fractures, information about the time at which the flow stops being linear is sometimes utilized. However, analysis techniques used in the industry oftentimes suffer from artifacts that distort well signals making it difficult to estimate reliably the end of linear flow as well as making it difficult to determine the type of boundary that follows. It could be impermeable rock surrounding the region stimulated by hydraulic fractures, also referred to as closed boundary, or a continuation of permeable rock after the region stimulated by hydraulic fractures, also referred to as an open boundary. Methodologies used in the industry can give the false impression of a closed boundary, which can incorrectly lead to application of boundary dominated type methods to estimate the amount of the subterranean resource for a non-existent boundary dominated flow and generate erroneous results. Poor decisions can be made when the end of linear flow and the type of boundary are not determined correctly, and estimates of the amount of subterranean resource (reserves) in a subterranean formation can be errorous.

Thus, there is a need in the industry for an improved way of determining the end of linear flow and the type of boundary more accurately. By doing so, the amount of the subterranean resource (reserves) of a reservoir can also be estimated more accurately.

SUMMARY

An embodiment of a computer implemented method of determining reserves of a reservoir includes receiving field data for a field that comprises a reservoir, wherein the field data includes pressure data and cumulative production data. The embodiment further includes generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data. The embodiment further includes generating a normalized pressure graph, wherein the normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values.

An embodiment of a computing apparatus includes at least one processor and at least one computer readable medium including computer readable instructions, that when executed by the at least one processor, cause performance of a method of determining reserves of a reservoir. The method includes method determining reserves of a reservoir includes receiving field data for a field that comprises a reservoir, wherein the field data includes pressure data and cumulative production data. The method further includes generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data. The method further includes generating a normalized pressure graph, wherein the normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values.

An embodiment of determining reserves of a reservoir includes identifying an end of the linear flow from a generated linear flow volume graph, wherein a stimulated reservoir volume equals linear flow volume corresponding to the end of the linear flow from the generated linear flow volume graph, and wherein the reserves of the reservoir are based on the stimulated reservoir volume, and wherein the generated linear flow volume graph is generated based on a slope and intercept from a generated normalized pressure graph that includes normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data. The embodiment further includes performing at least one field operation in response to the identified end of the linear flow from the generated linear flow volume graph.

These and other aspects, objects, features, and embodiments will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate only example embodiments and are therefore not to be considered limiting of its scope, as the disclosure may admit to other equally effective embodiments. The elements and features shown in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the example embodiments. Additionally, certain dimensions or positionings may be exaggerated to help visually convey such principles. In the drawings, reference numerals designate like or corresponding, but not necessarily identical, elements.

FIGS. 1A and 1B illustrate various views of a field system that includes a horizontal well in a hydraulically fractured reservoir with a plurality of fractures in accordance with certain example embodiments.

FIGS. 2A-2C illustrate portions of a hydraulically fractured reservoir with a plurality of hydraulic fractures. The Figures includes dashed lines to indicate the extension of the linear flow volume, as well as arrows describing the direction of flow in a reservoir at three different times.

FIGS. 3A-3D illustrate two examples. FIG. 3A illustrates a normalized pressure graph that can be generated according to this disclosure versus that obtained with conventional methodologies (FIG. 3B) for a well producing oil with a subterranean formation having hydraulic fractures. FIG. 3C illustrates a normalized pressure graph that can be generated according to this disclosure versus that obtained with conventional methodologies (FIG. 3D) for a well producing shale gas with a subterranean formation having hydraulic fractures.

FIGS. 4A-4B illustrate linear flow volume graphs. FIG. 4A corresponds to the oil producing well of FIG. 3A while FIG. 4B corresponds to the shale gas well of FIG. 3C.

FIG. 5 illustrates a diagram of a system in accordance with one or more example embodiments.

FIG. 6 illustrates a computing device in accordance with one or more example embodiments.

FIGS. 7A-7B illustrate a flowchart of a method in accordance with one or more example embodiments.

DETAILED DESCRIPTION

In the following detailed description includes example embodiments of determining reserves of a reservoir. A particular embodiment includes receiving field data for a field that includes a reservoir. The field data includes pressure data and cumulative production data. The particular embodiment further includes generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data, as well as generating a normalized pressure graph that includes a normalized pressure curve of the generated normalized pressure values.

For example, the detailed description includes example embodiments for determining reserves for a hydraulically fractured reservoir (e.g., with low permeability). A fractured reservoir is sometimes referred to as a fractured well. The terms “reservoir” and “subterranean formation” are used interchangeably herein. Indeed, the example embodiments relate to determining an amount of a subterranean resource in a drainage region of a producing hydraulically fractured reservoir. This drainage region of the reservoir, in which the subterranean resource flows linearly or linear flow volume (LFV), increases in size with time and it can be quantified with the embodiments presented in this disclosure. For example, the embodiments can include processing field data (e.g., flow rate and/or produced volume data together with downhole or surface pressure measurements) to calculate a quantity or variable named normalized pressure (e.g., normalized pressure values). The embodiments can include determining parameters from the normalized pressure variable to calculate the estimated size of the LFV of the reservoir as it changes with time. The size of this LFV can be converted to a volume generating a LFV curve. The embodiments can further include determining from the LFV curve the time at which the well stops producing mainly from the part of the reservoir enhanced by hydraulic fractures (e.g., end of linear flow) and starts producing mainly from surrounding reservoir. The embodiments can also include converting that linear flow volume to reserves. The embodiments can further include determining from the LFV curve whether the well has a closed boundary or an open boundary with a reservoir that extends beyond the region stimulated by the hydraulic fractures.

With a more accurate estimation of the reserves of a reservoir, a user can decide whether particular field operations should be performed and, if so, at what point in time the field operations should be performed. A field may include practically any formation (e.g., rock, sand, ice). The field operation is performed to reach and/or extract a subterranean resource and/or formation in certain example embodiments. Such a resource can include, but is not limited to, a hydrocarbon (e.g., oil, natural gas, a mixture of liquid and gas), coal, a metal, hydrogen, and water. The amount of a subterranean resource in a subterranean formation (e.g., a reservoir) can be called reserves of the subterranean resource. A field operation can also be related to finding (exploration) a subterranean formation that contains a resource or is used for storage of a resource (e.g., natural gas, carbon dioxide) according to certain example embodiments. Artificial fractures can be created in a subterranean formation using one or more of a number of methodologies, including but not limited to hydraulics. Fractures in a subterranean formation can provide permeability to allow the subterranean resource (e.g., natural gas, oil) to flow within the subterranean formation. In terms of recovering a subterranean resource, fracturing can allow a subterranean resource to flow into a production wellbore, where it can be extracted to the surface. Example embodiments described herein assume that the subterranean formation is already fractured.

Example embodiments will be described more fully hereinafter with reference to the accompanying drawings. Numerous specific details are set forth in order to provide a more thorough understanding of determining reserves of a reservoir, but it will be apparent to one of ordinary skill in the art that the claims are not limited to these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description. Further, certain descriptions (e.g., top, bottom, side, end, interior, inside) are merely intended to help clarify aspects of determining reserves of a reservoir (e.g., hydraulically fractured reservoir with low permeability) and are not meant to be limiting. However, determining reserves of a reservoir can be embodied in many different forms and should not be construed as limited to the example embodiments set forth herein. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of determining reserves in a fractured subterranean formation to those of ordinary skill in the art. Like, but not necessarily the same, elements (also sometimes called components) in the various figures are denoted by like reference numerals for consistency. Terms such as “first,” “second,” “distal,” “proximal,” “top,” “bottom,” “left,” “right,” “front,” and “back” are used merely to distinguish one component (or part of a component) from another. Such terms are not meant to denote a preference or a particular orientation.

FIGS. 1A and 1B illustrate various views of a field system that includes a horizontal well in a hydraulically fractured reservoir with a plurality of fractures in accordance with certain example embodiments. Specifically, FIG. 1A illustrates a schematic diagram of a land-based field system 100 having a subterranean production well or wellbore 120. The wellbore 120 is illustrated as horizontal, but could be vertical in another embodiment. The reservoir 110, near the wellbore 120, has been hydraulically fractured and has several fractures 192. Eight fractures 192 are illustrated in FIG. 1A. The fractures 192 are illustrated vertical with a height similar to the reservoir 110. The fractures 192 are visible in this view as lines more or less perpendicular to the wellbore 120. FIG. 1B illustrates a top view of a portion 101 of the subterranean production wellbore 120 that traverses a subterranean formation 109. The fractures 192 are visible in this view as lines more or less perpendicular to the wellbore 120. In one or more embodiments, one or more of the features shown in FIGS. 1A and 1B may be omitted, added, repeated, and/or substituted. Accordingly, embodiments of a field system having a fractured subterranean formation should not be considered limited to the specific arrangements of components shown in FIGS. 1A and 1B.

With continued reference to FIGS. 1A and 1B, the field system 100 in this example includes the wellbore 120 that is formed in the subterranean formation 109 using field equipment 130 above a surface 102, such as ground level for an on-shore application and the sea floor for an off-shore application. The point where the wellbore 120 begins at the surface 102 can be called the entry point. The subterranean formation 109 can include one or more of a number of formation zones. A formation zone can include one or more of a number of rock and/or formation types. Examples of such rock and/or formation types can include, but are not limited to, sand, limestone, clay, shale and salt. When a formation zone includes a subterranean resource, it can be called a reservoir 110. The reservoir can include fractured and unfractured portions, as well as include the subterranean resource, and this can be collectively referenced with “110”. The wellbore 120 can have one or more hydraulically created fractures 192 connecting the reservoir 110 to the wellbore 120. Each fracture 192 has its own length, height, and width. Width is likely very small compared to height and length.

FIG. 1B shows a top view of the wellbore 120 and the fractures 192. The wellbore 120 can be finished with casing 160. Inside the cavity of this casing 160, there can be production tubing 185 (also called a tubing string 185) that can be a number of tubing pipes that are mechanically coupled to each other end-to-end, usually with mating threads. However, in some embodiments, the wellbore 120 does not include tubing string.

Within a cavity 125, one or more packers and one or more seals can be included. For simplicity, these are illustrated as rectangle 180. The packers and seals of the rectangle 180 can be positioned hundreds or even thousands of feet away from the bottom of the wellbore 120. Below the packers and seals (toward the bottom of the wellbore 120) is a production zone 129 having a number of fractures 192 (which are created by forcing high-pressure fluid through perforations in the casing 160 during hydraulic fracturing). The perforations are not illustrated. The fractures 192 that extend from the casing 160 communicate the wellbore 120 with the reservoir 110. The fractures 192 allow production fluid (e.g., the subterranean resource 115) to flow from various parts of the reservoir 110 into the wellbore 120. In other words, the fractures 192 allow for communication between the reservoir 110 and the casing 160/wellbore 120.

As illustrated, the fractures 192 are assumed to be rectilinear and evenly spaced, and they are also assumed to have the same length and height. However, in some embodiments, the fractures 192 do not need to be as linear and/or evenly-spaced as shown in FIGS. 1A and 1B. For example, in some embodiments, the fractures 192 can intersect each other. Nonetheless, the permeability of the fractures 192 can increase permeability of the reservoir 110 as compared to an unfractured portion 115. The fractures 192 can be considered a physical extension of the wellbore 120.

FIGS. 2A-2C illustrate a portion of the reservoir 110 that includes a volume affected by extraction of the subterranean resource at three points in time during extraction of the subterranean resource. For example, each fracture 192 is associated with a corresponding volume that will be called linear flow volume (LFV) and each LFV is defined as the area inside a leading edge 277 located at particular distance from the fracture 192. The casing 160 and the hydraulic fractures 192 are illustrated in each of FIGS. 2A-2C as a reference. In FIG. 2A, the hydraulic fractures 192 make the flow 112 to occur perpendicularly to the fractures 192 and through an area of substantially the same size of the fractures 192. In other words, the subterranean resource flows linearly 112 during this linear flow period.

Returning to FIG. 2A, FIG. 2A illustrates the reservoir 110 at a time (e.g., the initial stages of extracting the subterranean resource) in which linear flow 112 of the subterranean resource prevails. At this time, each fracture 192 has an individual linear flow volume 111 affected by extraction of the subterranean resource. The linear flow volume 111 associated with each fracture 192 increases in size as the boundary 277 (denoted as “r”) moves farther away from the fractures 192. The linear flow volume 111 for the well that is calculated as shown below corresponds to the summation of the linear flow volumes of the individual fractures. The boundary 277 of the linear flow volume 111 is, for the most part, parallel to the hydraulic fracture 192 and expands outward over time as the drainage of the subterranean resource into the wellbore 120 progresses.

As illustrated in FIG. 2B, at some point in time, each boundary 277 cannot move anymore because each boundary 277 reaches the leading edge 277 and/or linear flow volume 111 of an adjacent fracture 192. In other words, the individual linear flow volumes 111 have merged into a single linear flow volume 111 of a size equal to the volume of the reservoir enhanced by hydraulic fractures. Flow that occurs after this time is not linear anymore and diverges from a straight line. This merged single linear volume 111 of the reservoir is called the Stimulated Reservoir Volume (SRV). The time that it takes for the merged single linear flow volume 111 to equal the SRV 292 is called the end of linear flow time. The SRV 292 is a fixed volume within the reservoir 110. The SRV 292 is substantially equal to the merged single linear flow volume 111 when the boundaries 277 of the individual linear flow volumes 111 of the fractures 192 are substantially merged into the single linear flow volume 111 (into one boundary 277).

In some instances, the reservoir 110 does not extend beyond the SRV 292. This can happen when impermeable rock is surrounding the SRV 292 or by the presence of other neighboring producing wells or wellbores that prevent the extension of the drainage volume for the wellbore 120. If this is the case, the boundary of the SRV is closed and flow is not linear anymore and becomes boundary dominated flow and its volume can be calculated using methodologies known to those of ordinary skill in the art.

However, in some instances, the reservoir 110 extends beyond the SRV 292. FIG. 2C illustrates the reservoir 110 at a time much larger than the end of linear flow time (i.e., when the merged single linear flow volume 111 equals the SRV, as shown in FIG. 2B). Specifically, the merged flow volume 111 continues to grow as the subterranean resource 115 continues to be extracted, becoming larger than the SRV 292 of FIG. 2B at this later time. Further, at this later time, the flow of the subterranean resource 112 becomes radial flow. In this case, the SRV 292 has a boundary that is open as the reservoir 110 continues beyond the SRV 292. Flow after the end of linear flow is not boundary dominated flow. There will likely be a small departure from linear flow volume behavior as will be shown below.

As discussed further in this disclosure, example embodiments allow the individual linear flow volumes 111, and eventually the SRV 292, to be determined without knowing the permeability of the rock in the reservoir 110 or the geometry of the fractures 192 in the reservoir 110. As long as the flow of the subterranean resource 112 is linear, example embodiments can be used to calculate the individual linear flow volumes 111 (that eventually form the merged single linear flow volume 111 that equals the SRV 292) over time.

As discussed further in this disclosure, by knowing the linear flow volumes 111 prior to the point in time of merger, the amount of subterranean resource inside the SRV 292 can be determined. One way of knowing the linear flow volumes 111 is by knowing the position of the leading edge 277 (boundary 277) of each linear flow volume 111 over time. However, prior to the point in time when the linear flow volumes 111 merge, the position of the leading edge 277 of the linear flow volumes 111 cannot be measured. Nonetheless, the example embodiments described herein illustrate how the linear flow volumes 111 can be calculated at a given time without knowing the position of the leading edge 277 or the permeability of the unfractured rock in the reservoir 110.

As discussed further in this disclosure, conventional methodologies rely on equivalent time (Q/q) rather than actual production time and this creates distortion and noise especially at late times as discussed below. Thus, conventional methodologies generally cannot provide an accurate estimate of the time when the flow continues to expand beyond the SRV 292. In reservoirs having very low permeability, such as that seen in shale rock, it can take years to reach the time when the merged single linear flow volumes 111 is equal to the SRV 292 (sometimes referred to as end of linear flow time). Prior to and when the merged single linear flow volume 111 equals the SRV 292, substantially all flow of the subterranean resource 112 is linear flow, but afterwards when the SRV 292 is exceeded, linear and/or non-linear flow of the subterranean resource 112 can occur. With the embodiments discussed herein, it can be possible to determine the time of end of linear flow as well as have an indication of the type of boundary that exists beyond the SRV. If the boundary is closed, it is possible to determine the size of the reservoir 110. If the boundary is open, it is possible to determine the size of the SRV 292.

Turning now to FIGS. 3A-3D, FIG. 3A illustrates a normalized pressure graph 300 that can be generated according to this disclosure versus that obtained with methodologies used in the industry (FIG. 3B) for a well producing oil with a subterranean formation having hydraulic fractures. FIG. 3C illustrates a normalized pressure graph 330 that can be generated according to this disclosure versus that obtained with methodologies used in the industry (FIG. 3D) for a well producing shale gas with a subterranean formation having hydraulic fractures.

Production history of a well or wellbore, such as the wellbore 120, can be analyzed using the following data: cumulative production at reservoir conditions (QB), initial reservoir pressure (p_(i)), and downhole flowing pressure (p_(wf)). If only surface pressure is available, then downhole flowing pressure can be calculated using methodologies known in the industry. Nonetheless, the reservoir pressure change is p=p_(i)−p_(wf) and the normalized pressure values can be defined as follows:

$\begin{matrix} {\frac{p}{q\; B} = {\frac{4}{\pi}\frac{p}{QB}t}} & (1) \end{matrix}$

where QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time in units (e.g., in days) appropriate to make the ratio QB/t have the proper units of flow rate (e.g., in bbl per day or bpd).

In Equation 1, t is time in units needed to make the ratio QB/t have the proper units of flow rate. This normalization technique was used to generate the normalized pressure graphs 300, 330 of FIGS. 3A, 3C, and this normalization technique can provide more accurate results than the currently used in the industry (FIGS. 3B, 3D) where normalized pressure is obtained by simply dividing pressure difference by flow rate qB. Real data typically has a lot of noise in the pressure and flow rates and simply dividing pressure by flow rate (as typically done in the industry) increases a lot the level of noise and hides the actual reservoir behavior. Although this problem can be mitigated by the use of integrals, there is an additional problem related to equivalent time with the methodology used in the industry as discussed below.

The normalized pressure values generated via Equation 1 are plotted versus actual production time. The production time is the time when the well is producing and periods when the well is shut in are excluded from the analysis. In the methodology used by the industry, an equivalent time different from actual time must be used. The equivalent time, or mass balance time, is defined as cumulative production divided by flow (Q/q). The use of equivalent time creates a problem when low flow rates are present in the records. Depending on variability of flow rate and pressure the resulting data can be very noisy and distorted particularly al late times when the flow rates are smaller. The reason is that low flow rates create very large equivalent times that frequently exceed the maximum actual production time and create distortion at late times sometimes creating an apparent closed boundary effect. This distortion makes it difficult to identify the end of linear flow.

FIGS. 3A, 3C and FIGS. 3B, 3D illustrate a comparison between the p/qb plots versus √{square root over (t)} using the methodology discussed herein (FIGS. 3A, 3C) and the conventional methodology (FIG. 3B, 3D). The scales are not shown, but the scales are the same in the pair of plots. Furthermore, a best fit line 305, 335 and an end of linear flow 310, 340 are illustrated in FIGS. 3A, 3C. The reason why the plots prepared with the conventional methodology (FIGS. 3B, 3D) look confusing is because of the use of equivalent time makes the points plot out of its sequence order in the data set. This means that points of earlier times can be plotted at late times and vice versa depending on the value of flow rate as it affects the calculated equivalent time (Q/q) Those plots illustrate that identifying the linear behavior characteristic of linear flow, as well as the point at which the plots deviate from linear (i.e., end of linear flow) is much easier to do with the embodiments discussed herein as illustrated in FIGS. 3A, 3C.

From the normalized pressure graph, like the one shown in FIG. 3A or 3C, the slope m and the intercept b can be determined. The value of n_(f)X_(f)√{square root over (t)} can be obtained from the slope m using Equation 2 as follows:

$\begin{matrix} {{n_{f}X_{f}\sqrt{k}} = {\frac{4.064}{hm}\sqrt{\frac{\mu}{\varphi \; c}}}} & (2) \end{matrix}$

wherein m is a slope (e.g., in psi/bpd/hr^(0.5)), h is the reservoir thickness (e.g., in ft), μ is viscosity (e.g., in cP), φ is porosity, k is permeability (e.g., in mD), n_(f) is a number of fractures (e.g., number of equally spaced fractures 192), X_(f) is a half-length of each of those fractures (e.g., in ft), and c is compressibility (e.g., in 1/psi).

Turning to FIGS. 4A and 4B, uncorrected linear flow volume values can be generated with Equation 3 as follows:

$\begin{matrix} {{LFV} = \frac{QB}{cp}} & (3) \end{matrix}$

Correction for skin can be done by using the values of slope m and intercept b obtained from the normalized pressure graph shown in FIGS. 3A, 3C. The correction and linear flow volume values can be generated using Equation 4 as follows:

$\begin{matrix} {{LFV} = {\frac{QB}{cp}\left( {1 + \frac{b}{m\sqrt{t}}} \right)}} & (4) \end{matrix}$

wherein QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time in units (e.g., in days) appropriate to make the ratio QB/t have the proper units of flow rate (e.g., in bbl per day or bpd), m is a slope, b is an intercept, and c is compressibility (e.g., in 1/psi).

Linear flow volume values can also be calculated for an infinite linear reservoir using Equation 5 as follows:

$\begin{matrix} {{LFV} = {{{1.305E} - {2\sqrt{\frac{\varphi}{\mu \; c}}{hn}_{f}X_{f}\sqrt{k}\sqrt{t}}} = \frac{\sqrt{t}}{6\; \pi \; m\; c}}} & (5) \end{matrix}$

where LFV is in bbl, and t in hours. The rest of the terms have been defined already. While the well is in linear flow, the LFV for an infinite reservoir is the same as that calculated volumetrically using Equation 4. The divergence of the LFV for an infinite reservoir (Equation 5) from the volumetrically calculated LFV (Equation 4) marks the end of linear flow. Moreover, the slope of the volumetrically calculated LFV tends to be flat when there is a closed boundary after the end of linear flow, but it illustrates a small reduction in slope when the boundary after the end of linear flow is open.

FIG. 4A illustrates the corresponding LFV curve for the oil well represented in FIG. 3A. The curve calculated with Equation 4 is presented, as well as the uncorrected curve calculated with Eq. 3 to illustrate the effect of the correction. In this example, the change is small because the skin pressure loss is small. Also presented is the LFV for an infinite reservoir calculated with Eq. 5. The time to end of linear flow (t_(elf)) is visible. The slope of the corrected LFV after t_(elf) illustrates a flattening of the LFV curve, which is characteristic of a closed boundary. The SRV equals the LFV value at the end of linear flow.

FIG. 4B illustrates the corresponding LFV curve for the shale gas well represented in FIG. 3C. In this example, the correction by skin is much more prominent. The point at which the corrected LFV curve diverges from the calculated one (Eq. 5) corresponds to the end of linear flow (t_(elf)). The SRV equals the LFV value at the end of linear flow. The slope of the corrected LFV after t_(elf) illustrates a small decrease in slope, which is characteristic of an open boundary and illustrates that the reservoir continues beyond the SRV.

In embodiments of the disclosure, because the linear flow volume 111 can be converted into reserves (an estimation of the subterranean resource 112), it is possible to construct a reserves curve versus time using example embodiments. These values can be obtained by dividing the linear flow volume 111 by the formation volume factor B.

Because the methodology using example embodiments is based on volumetric calculations, it can be used to estimate an amount of a subterranean resource in complex subterranean formations. For example, the distance between the casing 160 and the boundary between the linear flow volume 111 and the reservoir 110 does not need to have a rectangular shape. In addition, the hydraulic fractures 192 do not need to be parallel to each other. Using example embodiments, as long as there is linear flow it is possible to estimate the reserves, regardless of the actual geometry of the system and without knowledge of permeability, porosity, viscosity, and/or formation volume factor.

FIG. 5 illustrates a diagram of a system 600 in accordance with one or more example embodiments. The system 600 includes a computer system 602, a number of measuring devices (e.g., measuring device 1 660, measuring device N 662), and a user 650. The computer system 602 includes a subterranean resource determination application 604, a storage repository 630, a hardware processor 620, a memory 622, an application interface 626, and, optionally, a security module 628. The subterranean resource determination application 604 includes a calculation engine 606, a pore volume module 608, and an objective field operation module 610. The storage repository 630 can include formulas 632, field data 634, fracture data 636, and reservoir model data 638. Each of these components is described in further detail below. Example embodiments are not limited to the configuration shown in FIG. 5 and discussed herein. Additionally, although certain components have been enumerated as being part of the system 600, it is understood that some components are combined with other components and/or some components are further divided into additional components in other alternative example embodiments.

In one or more example embodiments, the computer system 602 is implemented according to a client-server topology. The computer system 602 may correspond to enterprise software running on one or more servers, and in some embodiments may be implemented as a peer-to-peer system, or resident upon a single computing system. In addition, the computer system 602 may be accessible from other machines using one or more application programming interfaces and/or user interfaces (not shown). In one or more example embodiments, the computer system 602 may be accessible over a network connection (not shown), such as the Internet, by one or more users 650. Further, information and/or services provided by the computer system 602 may also be stored and accessed over the network connection.

Alternatively or additionally, in one or more example embodiments, the computer system 602 is a local computer system of the user 650 and/or of one or more measuring devices (e.g., measuring device 1 660, measuring device N 662). In such embodiments, the computer system 602 is, optionally, not implemented using a client-server topology. For example, the computer system 602 corresponds to a laptop computer, desktop computer, mobile device, another type of computing device, or a combination of multiple computing devices. Additionally or alternatively, the computer system 602 is a distributed computer system and/or a multi-processor computer system in which the computer system includes multiple distinct computing devices.

Continuing with FIG. 5, the user 650 uses one or more subterranean reserves applications (not shown) to communicate with the computer system 602 in accordance with one or more example embodiments. For example, the user 650 receives a notification from the computer system 602 as to the simulated reservoir volume (SRV) for a particular subterranean formation. According to some example embodiments, the user 650 is an engineer, a company representative, a driller, a salesman, an agent, a broker, a consultant, a representative of a seller, an accountant, or some other entity with an interest in estimating the amount of reserves in a subterranean formation.

According to some example embodiments, the user 650 sends information (e.g., user preferences, settings, data) to the computer system 602 in a number of manners (e.g., modes of communication), including but not limited to the mail, a telephone, an email, a fax, a short message service, over the Internet, some other suitable mode for sending information, or any combination thereof. In certain example embodiments, the information sent by the user 650 to the computer system 602 is delivered automatically (e.g., according to a default setting, a consumer preference, an occurrence of an event) or on demand, for example, in response to a request from the computer system 602. The computer system 602 interacts with the user 650 in the same manner that the user 650 interacts with the computer system 602, or in a different manner using different modes of communication. The user 650 uses a user system (not shown), which is discussed below in further detail, to interact with the computer system 602 using software (not shown) in accordance with one or more example embodiments.

In one or more example embodiments, the user 650 interacts with one or more measuring devices (e.g., measuring device 1 660, measuring device N 662). Specifically and according to some example embodiments, the user 650 sends information (e.g., field data, fracture data) to and receives information from one or more measuring devices (e.g., measuring device 1 660, measuring device N 662).

In one or more example embodiments, the user 650 sends information to the measuring device 660, 662 in a number of manners (e.g., modes of communication), including but not limited to the mail, the telephone, the email, the fax, the short message service, over the Internet, some other suitable mode for sending information, or any combination thereof. Further, the user 650 receives information from the measuring device 660, 662 in some example embodiments. The information is delivered automatically (e.g., according to a default setting, a consumer preference, an occurrence of an event) or on demand, for example, in response to a request from the measuring device 660, 662. In certain example embodiments, the measuring device interacts with the user 650 in the same manner that the user 650 interacts with the measuring devices 660, 662, or in a different manner using different modes of communication. The user 650 uses the user system (not shown), which is described below in further detail, to interact with the measuring device 660, 662 using software (not shown) in accordance with one or more example embodiments.

In one or more example embodiments, each measuring device (e.g., measuring device 1 660, measuring device N 662) is an entity and/or system capable of receiving, sending, manipulating, and/or storing information associated with field data and/or fracture data. Examples of the measuring device 660, 662 include, but are not limited to, a model, a database, a spreadsheet, a sensing device (e.g., pressure sensor, flow rate monitor), a list of specifications, an operations plan, an accounting ledger, a financial table, and the user 650. A number of measuring devices 660, 662 can be used to receive, send, manipulate, and/or store information associated with the field data and/or the fracture data according to some example embodiments.

In one or more example embodiments, each measuring device (e.g., measuring device 1 660, measuring device N 662) sends information (e.g., field data, fracture data) to, and receives information (e.g., a request for field data) from, the computer system 602. The information is delivered automatically (e.g., according to a default setting, a marketing entity preference, an occurrence of an event) or on demand, as from a request made by the computer system 602. The data provided by the measuring devices 660, 662 includes, but is not limited to, pressure data, flow rates, physical characteristics of the reservoir, the geometry of the wellbore, and permeability. Examples of a measuring device can include, but are not limited to, a pressure sensor, a flow rate sensor, a temperature sensor, a wireline logging device, a spectrometer, and a rock analyzer.

Each measuring device 660, 662 interacts with the computer system 602 in the same mode of communication that the computer system 602 interacts with the measuring device 660, 662 or using different modes of communication in alternative example embodiments. In one or more example embodiments, each measuring device 660, 662 uses a measuring device system (not shown) to interact with the computer system 602 using measuring device software (not shown), which is discussed in further detail below. The computer system 602 also is implemented as a browser extension according to some example embodiments. In such a scenario, user software and/or measuring device software interacts directly with the computer system 602 as a browser extension.

Continuing with FIG. 5, the computer system 602 interacts with the user 650 and/or each measuring device (e.g., measuring device 1 660, measuring device N 662) using an application interface 626 in accordance with one or more example embodiments. Specifically, the application interface 626 of the computer system 602 receives input from and sends output to the user 650 and/or each measuring device 660, 662. The user 650 and/or each measuring device 660, 662 includes an interface to receive data from and send data to the computer system 602 in certain example embodiments. Examples of this interface include, but are not limited to, a graphical user interface, an application programming interface, a keyboard, a monitor, a mouse, a web service, a data protocol adapter, some other hardware and/or software, or any suitable combination thereof.

In one or more embodiments, the information received by the application interface 626 includes, but is not limited to, field data, fracture data, user preferences, settings, and feedback. The information sent by the application interface 626 includes, but is not limited to, a request for field data and a request for additional information. The information sent by the application interface 626 specifies, but is not limited to, a user, a field location, a measuring device, a Uniform Resource Identifier (URI) (e.g., a Uniform Resource Locator (URL), a web address, etc.), data identified by and/or requested by the calculation engine 606, some other software or source of information, or any suitable combination thereof.

In one or more example embodiments, the information (i.e., data) transferred among the application interface 626, the user 650, and/or each measuring device (e.g., measuring device 1 660, measuring device N 662) corresponds to metadata associated with such information. In this case, the metadata describes the data specified (i.e., the metadata provides context for the specified data). In one or more embodiments, the computer system 602 supports various data formats provided by the user 650 and/or each measuring device 660, 662.

Continuing with FIG. 5, the computer system 602 retrieves and stores formulas 632, field data 634, fracture data 636, and reservoir model data 638. More specifically, the computer system 602 uses the calculation engine 606 to retrieve and store formulas 632, field data 634, fracture data 636, and reservoir model data 638 in the storage repository 630 in accordance with one or more example embodiments.

In one or more example embodiments, a formula includes an equation (e.g., the equations 1-5 provided herein), set of parameters, or other means of using quantitative data to reach a numerical result. The formulas 632 of the storage repository 630 includes one or more formulas. Each formula is fixed in certain example embodiments, or is adjusted based on recent trends, user input, and/or any other information that affects the result produced by the formula in other example embodiments. A formula is directly or indirectly associated with field data and/or fracture data. A formula can be used to calculate flow, pressure, permeability, linear flow volume values, normalized pressure values, and/or production of the reservoir according to certain example embodiments. Examples of a number of formulas 632 are described in further detail herein.

In one or more example embodiments, the field data 634 of the storage repository 630 includes any data that is directly or indirectly associated with production of the reservoir. Field data 634 can be based on calculated, actual, and/or measured data. Examples of field data 634 can include, but are not limited to, pressure, flow rate, permeability, pressure data, cumulative production data, and physical characteristics of the reservoir.

In one or more example embodiments, the fracture data 636 of the storage repository 630 includes any data that is directly or indirectly associated with fractures in the subterranean formation. Fracture data 636 is based on data that is calculated, actual, and/or measured data. Examples of fracture data 636 include, but are not limited to, length of a fracture, width of a fracture, height of a fracture, age of a fracture, space between fractures, and number of fractures.

In one or more example embodiments, the reservoir model data 638 of the storage repository 630 includes any data that is directly or indirectly associated with the reservoir. Reservoir model data 638 can be any data, measured or calculated, associated with a reservoir, which can include the linear flow volume. Reservoir model data 638 can be specific to one or more reservoirs. Examples of reservoir model data 638 can include, but are not limited to, formations within the reservoir, properties (e.g., rock properties, size, permeability) of the various formations in the reservoir, wellbore depth, wellbore size(s), casing properties, and drill string properties.

Continuing with FIG. 5, the storage repository 630 is a persistent storage device (or set of devices) that stores software and data used to assist the calculation engine 606 in estimating an amount of reserves in a reservoir. In one or more example embodiments, the storage repository 630 stores the formulas 632, field data 634, fracture data 636, and reservoir model data 638. Examples of a storage repository 630 include, but are not limited to, a database (or a number of databases), a file system, a hard drive, some other form of data storage, or any suitable combination thereof. The storage repository 630 is located on multiple physical machines, each storing all or a portion of the formulas 632, field data 634, fracture data 636, and reservoir model data 638 according to some example embodiments. Each storage unit or device is physically located in the same or different geographic location.

The storage repository 630 is operatively connected to the subterranean resource determination application 604. In one or more example embodiments, the subterranean resource determination application 604 includes functionality to determine an amount of a subterranean resource 112 in a reservoir 110. More specifically, the subterranean resource determination application 604 sends information to and/or receives information from the storage repository 630 in order to determine an amount of a subterranean resource 112 in a reservoir 110.

The functions of the subterranean resource determination application 604 can be performed on a single computing device or on multiple computing devices. When the functions of the subterranean resource determination application 604 are performed on multiple computing devices, a number of configurations and/or frameworks are used in certain example embodiments. The configurations and/or software frameworks are designed to work with multiple data nodes and large quantities of data. One or more calculations performed by one or more components of the subterranean resource determination application 604 are performed on multiple machines operating in parallel, where the results from each machine are combined to generate a result to the one or more calculations.

Each component of the subterranean resource determination application 604 described herein (specifically, the calculation engine 606, the pore volume module 608, and the field operation module 610) uses one or more algorithms (which can include one or more steps) to perform one or more calculations. Each algorithm is designed to receive specific types of data and generate one or more specific results using such data. A specific result is a number, a range of numbers, a rating, and/or some other suitable output according to some example embodiments. Each algorithm can be fixed, variable, self-adjusting, or otherwise changed. Each algorithm uses one or more pieces of data from one or more sources of data (e.g., field data, fracture data, and reservoir model data).

In one or more embodiments, the calculation engine 606 of the subterranean resource determination application 604 coordinates the field operation module 610, the pore volume module 608, the storage repository 630, and, optionally, the security module 628. Specifically, the calculation engine 606 coordinates the transfer of information between the application interface 626, the storage repository 630, and the other components of the subterranean resource determination application 604 according to certain example embodiments.

Further, the calculation engine 606 also retrieves the formulas 632, the field data 634, the fracture data 636, and the reservoir model data 638 from, and sends the formulas 632, the field data 634, the fracture data 636, and the reservoir model data 638 to the storage repository 630 for use by the calculation engine 606 or by other components of the subterranean resource determination application 604. The calculation engine 606 also retrieves the formulas 632, the field data 634, the fracture data 636, and the reservoir model data 638 from the storage repository 630 to be sent to the user 650 and/or one or more measuring devices 660, 662.

Continuing with FIG. 5, the calculation engine 606 retrieves, in example embodiments, information needed and/or requested by the field operation module 610 and/or the contacted pore volume module 608. The calculation engine 606 retrieves specific types of information (e.g., geological data) from the data repository 630 and/or one or more specific measuring devices 660, 662. Alternatively, the calculation engine 606 queries all measuring devices 660, 662 and the storage repository 630 for any information needed and/or requested by the field operation module 610 and/or the pore volume module 608.

In certain example embodiments, the calculation engine 606 receives data (e.g., field data, fracture data, reservoir model data, any other suitable type of data) from the one or more measuring devices (e.g., measuring device 1 660, measuring device N 662). The calculation engine 606 also sends a request for data to the one or more measuring devices 660, 662 in certain example embodiments. A request is for a specific type of data in some example embodiments. A request also is sent to a specific measuring device 660, 662 according to some example embodiments. A request is sent based on one or more of a number of events, including but not limited to passage of time and a need identified by a module (e.g., the pore volume module 608, the field operation module 610). Any request sent and/or data received by the calculation engine 606 is executed using the application interface 626.

The calculation engine 606 also sends data to, and receives data from, each of the modules (the pore volume module 608, the field operation module 610) of the subterranean resource determination application 604. The data received from a module includes results after executing a model of the respective module according to some example embodiments. The calculation engine 606 further compares the results received from one or more modules with one or more criteria. Alternatively, or in addition, as discussed below, one or more modules compares the results generated by one or more modules with one or more criteria.

In one or more example embodiments, the calculation engine 606 also determines an amount of the subterranean resource 112 at a point in time based on a pore volume 111 at the point in time received from the pore volume module 608. In such a case, the calculation engine 606 can use one or more formulas 632 to determine an amount of the subterranean resource 112 at various points in time based on the pore volume 111 at those points in time. The formulas 632 used by the calculation engine 606 can include one or more linear flow equations and/or one or more non-linear (e.g., radial, spherical) flow equations for a particular point in time.

The determination performed by the calculation engine 606 can be based on field data collected by one or more measuring devices (e.g., measuring device 1 660, measuring device N 662). The calculation engine 606 can evaluate the reservoir 110 using a cumulative production data and pressure data (or some other medium within the field system 100).

As stated above, the calculation engine 606 can use one or more formulas 632 in making its determination of the amount of the subterranean resource 112 at a point in time. Different formulas 632 can be used when the calculation engine 606 evaluates the amount of the subterranean resource 112 at different points in time. Alternatively, the same formula, using different parameters, can be used by the calculation engine 606 to evaluate the amount of the subterranean resource 112 at different points in time. Examples of such formulas 632 are described above with respect to FIGS. 3A-3D and FIGS. 4A-4B. One or more of the formulas 632 can be based on a number of variables, including but not limited to time, pressure, cumulative produced volume, and compressibility. The size of each portion of the reservoir 110 evaluated by the calculation engine 606 can change over time. For example, as shown in FIGS. 2A-2C above, the size of the linear pore volume 111 can increase over time.

In certain embodiments, the calculation engine 606 also sends a notification. Specifically, the calculation engine 606 can send a notification to the user 650 to illustrate the user 650 the amount of the subterranean resource 112 at one or more points in time. The calculation engine 606 can also send one or more other types of notifications, including but not limited to a recommended field operation generated by the field operation module 610. Any notification sent by the calculation engine 606 can include other supporting data, including but not limited to a summary (e.g., a graph, a table) of the total amount of the subterranean resource 112 and a summary of the recommended field operation.

In one or more example embodiments, the pore volume module 608 determines the linear flow volume 111 within the reservoir 110 at a point in time. The pore volume module 608 can determine the linear flow volume 111 at a single point in time, at a number of discrete points in time, and/or continuously over a range of times. The pore volume module 608 can use fracture data 636 when determining the linear flow volume 111. In addition, or in the alternative, the pore volume module 608 can use formulas 632, field data 634, and/or reservoir model data 638 to determine the linear flow volume 111.

In one or more example embodiments, the field operation module 610 recommends one or more field operations to perform in the reservoir 110. The field operation that the field operation module 610 recommends can be based, at least in part, on the total amount of the subterranean resource 112 (and/or an amount of one or more portions of the reservoir 110) generated by the calculation engine 606. In addition, or in the alternative, the field operation module 610 can recommend a field operation based on formulas 632, field data 634, and/or reservoir model data 638.

Continuing with FIG. 5, the hardware processor 620 within the computer system 602 executes software in accordance with one or more embodiments of the invention. Specifically, the hardware processor 620 can execute the computer system 602 or any of the engines, modules, and repositories described above and shown in FIG. 5, as well as software used by the user 650 and/or one or more measuring devices 660, 662. The hardware processor 620 is an integrated circuit, a central processing unit, a multi-core processing chip, a multi-chip module including multiple multi-core processing chips, or other hardware processor in one or more example embodiments. The hardware processor 620 is known by other names, including but not limited to a computer processor, a microprocessor, and a multi-core processor. In one or more embodiments of the invention, the hardware processor 620 executes software instructions stored in memory 622. The memory 622 includes one or more cache memories, main memory, and/or any other suitable type of memory. The memory 622 is discretely located on the computer system 602 relative to the hardware processor 620 according to some example embodiments. In certain configurations, the memory 622 also is integrated with the hardware processor 620.

Optionally, in one or more example embodiments, the security module 628 secures interactions between the computer system 602 and the user 650 and/or the measuring devices 660, 662. More specifically, the security module 628 authenticates communication from software based on security keys verifying the identity of the source of the communication. For example, user software may be associated with a security key enabling the user software to interact with the computer system 602. Further, the security module 628 restricts receipt of information, requests for information, and/or access to information in some example embodiments.

The user software and/or measuring device software interacts with the computer system 602 using a browser extension. In this case, the browser extension maintains an active session with the computer system 602 after the security module 628 has authenticated the user software and/or measuring device software. For example, the browser extension continues to interact with the computer system 602 as the user 650 views various web content in the user software. In this example, the browser extension receives notifications from the computer system 602 for presenting to the user 650.

As discussed above, the user 650 and measuring devices 660, 662 can use a user system and measuring device system, respectively, in certain example embodiments. One or more of the user system and measuring device system is, or contains a form of, an Internet-based or an intranet-based computer system that is capable of communicating with the applicant software. A computer system includes any type of computing device and/or communication device, including but not limited to, the computer system 602. Examples of the user system and measuring device system includes, but are not limited to, a desktop computer with Internet or intranet access, a laptop computer with Internet or intranet access, a smart phone, a server, a server farm, and a personal digital assistant (PDA). The user system and/or measuring device system correspond to a computer system as described.

Further, as discussed above, the user system and/or measuring device system each have corresponding software (e.g., user software and measuring device software, respectively). The user software and measuring device software execute on a separate device (e.g., a server, mainframe, desktop personal computer (PC), laptop, personal desktop assistant (PDA), television, cable box, satellite box, kiosk, telephone, mobile phone, or other computing devices) from the computer system 602, the user 650 and/or the one or more measuring devices 660, 662, and is coupled by a network (e.g., Internet, Intranet, Extranet, Local Area Network (LAN), Wide Area Network (WAN), or other network communication methods), with wire and/or wireless segments according to some example embodiments. The user software also is part of, or operates separately but in conjunction with, the computer system 602 and/or the one or more measuring devices 660, 662.

In one or more example embodiments, one or more of the user software and measuring device software displays web page(s) (i.e., web content). More specifically, the user software and measuring device software is any software capable of rendering Hypertext Markup Language (HTML) in one or more example embodiments. For example, the user software and measuring device software is a web browser(s) used by the corresponding system to access web pages (i.e., web content) over the Internet (or other Wide Area Network or Local Area Network). One or more of the user software and measuring device software also displays data in other formats, including but not limited to JavaScript™, JavaScript™ Object Notation (JSON) and XML. (JavaScript is a registered trademark and service mark of Oracle America, Inc. of Redwood Shores, Calif.)

In one or more example embodiments, one or more of the user software and measuring device software provides support for browser extension(s). More specifically, one or more of the user software and measuring device software provide an open framework (i.e., software design that allows for easy removal, addition, and/or replacement of software components) for adding features to the user software and/or measuring device software. In this case, a browser extension is an application that extends the functionality of the software using the open framework. The user software interacts with the computer system 602 and/or the one or more measuring devices 660, 662 using the browser extension(s). Further, the browser extension(s) interacts with a user interface of the user software (as well as a measuring device interface of measuring device software).

FIG. 6 illustrates one embodiment of a computing device 800 that implements one or more of the various techniques described herein, and which is representative, in whole or in part, of the elements described herein pursuant to certain example embodiments. Computing device 800 is one example of a computing device and is not intended to suggest any limitation as to scope of use or functionality of the computing device and/or its possible architectures. Neither should computing device 800 be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the example computing device 800.

Computing device 800 includes one or more processors or processing units 802, one or more memory/storage components 804, one or more input/output (I/O) devices 806, and a bus 808 that allows the various components and devices to communicate with one another. Bus 808 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. Bus 808 includes wired and/or wireless buses.

Memory/storage component 804 represents one or more computer storage media. Memory/storage component 804 includes volatile media (such as random access memory (RAM)) and/or nonvolatile media (such as read only memory (ROM), flash memory, optical disks, magnetic disks, and so forth). Memory/storage component 804 includes fixed media (e.g., RAM, ROM, a fixed hard drive, etc.) as well as removable media (e.g., a Flash memory drive, a removable hard drive, an optical disk, and so forth).

One or more I/O devices 806 allow a customer, utility, or other user to enter commands and information to computing device 800, and also allow information to be presented to the customer, utility, or other user and/or other components or devices. Examples of input devices include, but are not limited to, a keyboard, a cursor control device (e.g., a mouse), a microphone, and a scanner. Examples of output devices include, but are not limited to, a display device (e.g., a monitor or projector), speakers, a printer, and a network card.

Various techniques are described herein in the general context of software or program modules. Generally, software includes routines, programs, objects, components, data structures, and so forth that perform particular tasks or implement particular abstract data types. An implementation of these modules and techniques are stored on or transmitted across some form of computer readable media. Computer readable media is any available non-transitory medium or non-transitory media that is accessible by a computing device. By way of example, and not limitation, computer readable media includes “computer storage media”.

“Computer storage media” and “computer readable medium” include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules, or other data. Computer storage media include, but are not limited to, computer recordable media such as RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which is used to store the desired information and which is accessible by a computer.

The computer device 800 is connected to a network (not shown) (e.g., a local area network (LAN), a wide area network (WAN) such as the Internet, or any other similar type of network) via a network interface connection (not shown) according to some example embodiments. Those skilled in the art will appreciate that many different types of computer systems exist (e.g., desktop computer, a laptop computer, a personal media device, a mobile device, such as a cell phone or personal digital assistant, or any other computing system capable of executing computer readable instructions), and the aforementioned input and output means take other forms, now known or later developed, in other example embodiments. Generally speaking, the computer system 800 includes at least the minimal processing, input, and/or output means necessary to practice one or more embodiments.

Further, those skilled in the art will appreciate that one or more elements of the aforementioned computer device 800 is located at a remote location and connected to the other elements over a network in certain example embodiments. Further, one or more embodiments is implemented on a distributed system having one or more nodes, where each portion of the implementation (e.g., calculation engine 606, fracture volume module 608) is located on a different node within the distributed system. In one or more embodiments, the node corresponds to a computer system. Alternatively, the node corresponds to a processor with associated physical memory in some example embodiments. The node alternatively corresponds to a processor with shared memory and/or resources in some example embodiments.

Although the application 604 and modules thereof are described herein (e.g., in the context of FIG. 5), those of ordinary skill in the art will appreciate that the disclosure is not limited to this example, and hardware, software, instructions, program code (e.g., data and instructions), multiple applications, any combination thereof, etc. can be used. Indeed, instructions can include routines, programs, objects, components, data structures, and so forth that perform particular tasks or implement particular abstract data types. Thus, at least one processor and a computer readable medium including the instructions, that when executed by the at least one processor, cause performance of a method for determining reserves of a reservoir.

One or more example embodiments provide a more accurate estimate of the amount of subterranean resources in a reservoir (e.g., a low permeability reservoir with artificial fractures). Based on this estimate of the amount of the subterranean resource, one or more recommended field operations can be generated in certain example embodiments.

FIGS. 7A-7B illustrate a flowchart of an embodiment of method 1000 for determining an amount of a subterranean resource in a reservoir in accordance with one or more example embodiments. While the various items in this flowchart are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the items are executed in different orders, combined or omitted, and some or all of the items are executed in parallel depending upon the example embodiment. Further, in one or more of the example embodiments, one or more of the items described below are omitted, repeated, and/or performed in a different order.

In addition, a person of ordinary skill in the art will appreciate that additional items not shown in FIGS. 7A-7B, are included in performing this method in certain example embodiments. Accordingly, the specific arrangement of items should not be construed as limiting the scope. In addition, a particular computing device, as described, for example, in FIGS. 5-6, is used to perform one or more of the items for the method 1000 described below in certain example embodiments.

Now referring to FIGS. 7A-7B, the example method 1000 begins at the START item and proceeds to item 1005 to receive field data for a field that comprises a reservoir. The field data includes pressure data and cumulative production data. The cumulative production data includes cumulative production, which is the total volume produced by a well or wellbore (e.g., the wellbore 120) since the start of operations. The pressure data includes pressure, which is the difference between initial downhole pressure and flowing pressure.

In certain example embodiments, the field data is received by the calculation engine 606 and stored as field data 634 in the storage repository 630. The reservoir 110 can be part of a field (e.g., a subterranean formation 109). The field data can be collected by and/or received from one or more of a number of measuring devices (e.g., measuring device 1 660, measuring device N 662). The field data can be received based on an inquiry (sent, for example, by the calculation engine 606 of the subterranean resource determination application 604). Alternatively, or in addition, the field data can be received continuously or at some periodic interval. The field data can correspond, or be taken at, a certain point in time (e.g., a first time). In certain example embodiments, the point in time in which the field data is taken is prior to when the merged single linear flow volume 111 is substantially equal to the SRV 292.

At item 1010, normalized pressure values are generated for a plurality of timestamps using time, the pressure data, and the cumulative production data. For example, the normalized pressure values can be generated or calculated using Equation 1 as follows:

$\begin{matrix} {\frac{p}{qB} = {\frac{4}{\pi}\frac{p}{QB}t}} & (1) \end{matrix}$

wherein QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time in units (e.g., in days) appropriate to make the ratio QB/t have the proper units of flow rate (e.g., bbl per day or bpd).

At item 1015, a normalized pressure graph is generated. The normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values. For example, the normalized pressure graphs 300 in FIG. 3A and 330 in FIG. 3C include normalized pressure curves 307 and 337, respectively, of the generated normalized pressure values labeled as calculated. Those of ordinary skill in the art will appreciate that the normalized pressure graphs 300 in FIG. 3A and 330 in FIG. 3C are improvements over graphs 315 in FIG. 3B and 345 in FIG. 3D that are generated using conventional methodologies. The normalized pressure graphs 300 and 330 can be plotted versus square root of the time (e.g., in hours).

At item 1020, a slope and an intercept can be determined from the generated normalized pressure graph. More specifically, the slope and the intercept can be determined from the generated pressure graph versus square root of the time in hours (e.g., from item 1015). For example, the slope m can be in psi/bpd/hr^(0.5) and the intercept b can be in psi/bpd. The slope m and the intercept b (e.g., y-intercept) can be calculated in an automated manner using Equation 6 as follows:

y=mx+b  (6)

wherein m is a slope, b is an intercept, and x and y are values corresponding to the x axis and y axis, respectively.

Item 1025 includes applying simple linear regression to obtain a best fit line to a linear portion of the generated normalized pressure graph, and wherein determining the slope and the intercept from the generated normalized pressure graph includes using the best fit line. In some embodiments, the linear regression can be a regression other than simple linear regression. The slope m can be in psi/bpd/hr^(0.5) and the intercept b can be in psi/bpd, and the slope and the intercept determined in item 1020 can be utilized. The best fit line is illustrated as the linear fit line 305 in FIG. 3A and the linear fit line 335 in FIG. 3C.

Item 1030 includes determining an end of linear flow from the generated normalized pressure graph using the best fit line. For example, in FIG. 3A, the end of linear flow 310 can be determined from the generated normalized pressure graph when the normalized pressure curve 307 deviates from the best fit line (e.g., the linear fit line 305) using derivatives, a threshold, or both. A deviation indicates the end of linear flow 310. Similarly, the end of linear flow 340 in FIG. 3C can be determined when the normalized pressure curve 337 deviates from the best fit line (e.g., the linear fit line 335) using derivatives, a threshold, or both. A deviation indicates the end of linear flow 340.

Regarding the derivatives, the derivatives can be log time derivatives. Specifically, the log time derivatives can be used to help identify the change in slope (i.e., the end of linear flow). The log time derivatives can lead to generation of a derivatives line that indicates the change in the slope more clearly. In an automated manner, the derivatives can be calculated at tdp/dt, and it is the slope of the line multiplied by the time that can be used to automatically determine the end of linear flow. Of note, in some embodiments, a derivatives line can be calculated and plotted in an automated manner, and a user can then visually determine the end of linear flow. Alternatively, or additionally, derivatives used in oil and gas pressure transient analysis can be utilized at item 1030.

Regarding the threshold, a deviation from the threshold indicates the end of linear flow. The threshold can be a range or a specific value. For example, the threshold can be a minimum value of change, and in an automated manner, a determination can be made as to whether the slope changed more than the minimum value of change (i.e., the threshold). If the slope changed more than the minimum value of change, then the end of linear flow has been determined.

Item 1035 includes generating linear flow volume values for the timestamps using the determined slope and the determined intercept, and generating a linear flow volume graph, wherein the linear flow volume graph includes a linear flow volume curve of the generated linear flow volume values. For example, generating the linear flow volume values includes using an equation. For example, the following Equation 4 can be used:

$\begin{matrix} {{LFV} = {\frac{QB}{cp}\left( {1 + \frac{b}{m\sqrt{t}}} \right)}} & (4) \end{matrix}$

wherein QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time (e.g., in units such as days appropriate to make the ratio QB/t have the proper units of flow rate (e.g., in bbl per day or bpd)), m is a slope, b is an intercept, and c is compressibility (e.g., in 1/psi). Examples of linear flow volume curves are illustrated as linear flow volume graphs 400 in FIG. 4A and 420 in FIG. 4B.

Item 1040 includes generating a theoretical linear flow volume line for an infinite linear reservoir; and applying the theoretical linear flow volume line to the generated linear flow volume graph. For example, generating the theoretical linear flow volume line for an infinite linear reservoir includes using an equation. For example, the following equation can be used:

${LFV} = {{{1.305E} - {2\sqrt{\frac{\varphi}{\mu \; c}}{hn}_{f}X_{f}\sqrt{k}\sqrt{t}}} = \frac{\sqrt{t}}{6\; \pi \; m\; c}}$

wherein LFV is pore volume (e.g., in bbl), t is time (e.g., in hrs), m is a slope (e.g., the slope of the normalized pressure curve 307 (e.g., in psi/bpd/hr^(0.5))), c is compressibility (e.g., in 1/psi), h is reservoir thickness (e.g., in ft), μ is viscosity (e.g., in cP), φ is porosity, k is permeability (e.g., in mD), n_(f) is a number of fractures (e.g., number of equally spaced fractures 192), and X_(f) is a half-length of each of those fractures (e.g., in ft). An example of the theoretical linear flow volume line is illustrated in the linear flow volume graph 400 in FIG. 4A as LFV corrected.

Item 1045 includes determining an end of linear flow using the theoretical linear flow volume line. For example, determining the end of linear flow includes determining when the linear flow volume curve deviates from the theoretical linear flow volume line for an infinite linear reservoir using derivatives, a threshold, or both, wherein a deviation indicates the end of linear flow. An example of the end of linear flow is illustrated in the linear flow volume graph 400 in FIG. 4A as the end of linear flow 410 and as the end of linear flow 430 in FIG. 4B. The end of linear flow determined at item 1045 should coincide with the end of linear flow determined in Item 1030. The discussion of derivatives and threshold at item 1030 applies to the item 1045.

Item 1050 includes determining the reserves of the reservoir using a stimulated reservoir volume, wherein the stimulated reservoir volume (SRV) equals the linear flow volume corresponding to the end of the linear flow from the generated linear flow volume graph. The end of linear flow is illustrated as the end of linear flow 410 in the generated linear flow volume graph 400 of FIG. 4A and the end of linear flow 430 in the generated linear flow volume graph 420 of FIG. 4B. The SRV of FIG. 4A equals the linear flow volume corresponding to the end of linear flow 410 and the SRV of FIG. 4B equals the linear flow volume corresponding to the end of linear flow 430. The SRV is a reservoir volume (e.g., a pore volume) and it can be expressed in barrels. Reserves can be calculated by dividing this volume by a formation volume factor B that converts surface volume to downhole volume. Reserves are expressed in standard barrel. Normally oil shrinks when taken to the surface and gas expands so the formation volume so the factor B is utilized. In short, reserves=(reservoir pore volume)/factor B, wherein the units of factor B are reservoir bbl/standard bbl, and wherein standard means at standard conditions (e.g., 60 F and 1 atmosphere os pressure).

Item 1055 includes using a shape of the linear flow volume curve after end of linear flow from the generated linear flow volume graph to facilitate determination of a type of boundary after the end of linear flow from the generated linear flow volume graph. For example, if the generated linear flow volume graph becomes flat, then there is a closed boundary. However, if the generated linear flow volume graph only shows a small decrease in slope, then it is an open boundary. A threshold, a range, or the like can be utilized to use the shape to determine the type. How small of a change in the shape can depend on the embodiment (e.g., how much certainty is desired). The boundary can be open or closed. In some embodiments, the boundary can even be partially open, and thus, more data may be needed. Alternatively, or additionally, a user can visually inspect the shape and determine the type of the boundary.

Item 1060 includes modifying a reserve value based on the type of boundary after the end of linear flow from the generated linear flow volume graph, a stimulated reservoir volume, or any combination thereof, wherein the stimulated reservoir volume equals the linear flow volume corresponding to the end of the linear flow from the generated linear flow volume graph. For example, a pre-existing reserve value can be modified based on the item 1050.

Those of ordinary skill in the art will appreciate that various modifications can be made to the method 1000. For example, the terminology “a slope” or “an intercept” is utilized in defining terms of an equation, however, the value of the slope and the intercept, in some instances, has already been determined in a previous equation (or in a previous item or step). For example, the generated linear flow volume graphs of FIGS. 4A-4B can rely on the slope and intercept of the generated normalized pressure graphs of FIGS. 3A and 3C.

Furthermore, although the method 1000 is a computer implemented method that can be implemented using FIG. 5 and/or FIG. 6, one or more items can be performed visually identified by a user. Therefore, additionally or alternatively, a user can manually determine the end of linear flow, the slope, the best fit line, and/or the intercept from the generated normalized pressure graphs of FIGS. 3A and 3C by visually identifying these from the generated normalized pressure graphs of FIGS. 3A and 3C. Similarly, additionally or alternatively, a user can manually determine the end of linear flow and/or the SRV of FIGS. 4A and 4B by visually identifying these from the generated linear flow volume graphs of FIGS. 4A-4B. Furthermore, some embodiments can include both automated aspects performed by a computing apparatus and manual aspects performed by a user. More information can also be found in the following paper that is incorporated herein by reference in its entirety and for all purposes: Jorge A. Acuña, Application of Linear Flow Volume to Rate Transient Analysis, SPE 173330-MS, SPE Hydraulic Fracturing Technology Conference held in The Woodlands, Tex., USA, 3-5 Feb. 2015.

Indeed, although determining an amount of reserves in a low permeability reservoir with a fractured well is described with reference to some example embodiments, it should be appreciated by those skilled in the art that various modifications are well within the scope of determining an amount of reserves in a reservoir. From this disclosure, it will be appreciated that an embodiment of determining an amount of reserves in low permeability reservoir with a fractured well using only cumulative production, pressure and compressibility overcomes the limitations of the prior art. Those skilled in the art will appreciate that the normalization technique for variable pressure and flow is not limited to any specifically discussed application and that the example embodiments described herein are illustrative and not restrictive. From the description of the example embodiments, equivalents of the elements shown therein will suggest themselves to those skilled in the art, and ways of constructing other embodiments of determining an amount of reserves in low permeability reservoir with a fractured well will suggest themselves to practitioners of the art. Therefore, the scope of determining an amount of reserves in a low permeability reservoir with a fractured well is not limited herein. 

1. A computer implemented method of determining reserves of a reservoir, the method comprising: receiving field data for a field that comprises a reservoir, wherein the field data includes pressure data and cumulative production data; generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data; and generating a normalized pressure graph, wherein the normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values.
 2. The method of claim 1, wherein generating the normalized pressure values includes using an equation, wherein the equation is: $\frac{p}{qB} = {\frac{4}{\pi}\frac{p}{QB}t}$ wherein QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time in units appropriate to make ratio QB/t have proper units of flow rate.
 3. The method of claim 1, further comprising determining a slope and an intercept from the generated normalized pressure graph.
 4. The method of claim 3, further comprising applying simple linear regression to obtain a best fit line to a linear portion of the generated normalized pressure graph, and wherein determining the slope and the intercept from the generated normalized pressure graph includes using the best fit line.
 5. The method of claim 4, further comprising determining an end of linear flow from the generated normalized pressure graph using the best fit line.
 6. The method of claim 5, wherein determining the end of linear flow from the generated normalized pressure graph includes determining when the normalized pressure curve deviates from the linear fit line using derivatives, a threshold, or both, wherein a deviation indicates the end of linear flow.
 7. The method of claim 3, further comprising: generating linear flow volume values for the timestamps using the determined slope and the determined intercept from the generated normalized pressure graph, and generating a linear flow volume graph, wherein the linear flow volume graph includes a linear flow volume curve of the generated linear flow volume values.
 8. The method of claim 7, wherein generating the linear flow volume values includes using an equation, wherein the equation is: ${LFV} = {\frac{QB}{cp}\left( {1 + \frac{b}{m\sqrt{t}}} \right)}$ wherein QB is cumulative production at reservoir conditions, p_(i) is initial reservoir pressure, p_(wf) is downhole flowing pressure, p=p_(i)−p_(wf) is reservoir pressure change, and t is time, m is a slope, b is an intercept, and c is compressibility.
 9. The method of claim 8, further comprising: generating a theoretical linear flow volume line for an infinite linear reservoir; and applying the theoretical linear flow volume line to the generated linear flow volume graph.
 10. The method of claim 9, wherein generating the theoretical linear flow volume line for an infinite linear reservoir includes using an equation, wherein the equation is: ${LFV} = {{{1.305E} - {2\sqrt{\frac{\varphi}{\mu \; c}}{hn}_{f}X_{f}\sqrt{k}\sqrt{t}}} = \frac{\sqrt{t}}{6\; \pi \; m\; c}}$ wherein LFV is pore volume, t is time, m is a slope, c is compressibility, h is reservoir thickness, μ is viscosity, φ is porosity, k is permeability, n_(f) is a number of fractures, and X_(f) is a half-length of each of those fractures.
 11. The method of claim 9, further comprising determining an end of linear flow from the generated linear flow volume graph using the theoretical linear flow volume line.
 12. The method of claim 11, wherein determining the end of linear flow from the generated linear flow volume graph includes determining when the linear flow volume curve deviates from the theoretical linear flow volume line for the infinite linear reservoir using derivatives, a threshold, or both, wherein a deviation indicates the end of linear flow.
 13. The method of claim 11, further comprising determining the reserves of the reservoir using a stimulated reservoir volume, wherein the stimulated reservoir volume equals the linear flow volume corresponding to the end of the linear flow from the generated linear flow volume graph.
 14. The method of claim 11, further comprising using a shape of the linear flow volume curve after end of linear flow from the generated linear flow volume graph to facilitate determination of a type of boundary after the end of linear flow from the generated linear flow volume graph.
 15. A computing apparatus, the apparatus comprising: At least one processor; and At least one computer readable medium including computer readable instructions, that when executed by the at least one processor, cause performance of a method of determining reserves of a reservoir, the method comprising: receiving field data for a field that comprises a reservoir, wherein the field data includes pressure data and cumulative production data; generating normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data; and generating a normalized pressure graph, wherein the normalized pressure graph includes a normalized pressure curve of the generated normalized pressure values.
 16. The apparatus of claim 15, the method further comprising: generating linear flow volume values for the timestamps using a determined slope and a determined intercept from the generated normalized pressure graph, and generating a linear flow volume graph, wherein the linear flow volume graph includes a linear flow volume curve of the generated linear flow volume values.
 17. The apparatus of claim 16, the method further comprising: determining the reserves of the reservoir using a stimulated reservoir volume, wherein the stimulated reservoir volume equals a linear flow volume corresponding to an end of the linear flow from the generated linear flow volume graph.
 18. A method of determining reserves of a reservoir, the method comprising: identifying an end of the linear flow from a generated linear flow volume graph, wherein a stimulated reservoir volume equals linear flow volume corresponding to the end of the linear flow from the generated linear flow volume graph, and wherein the reserves of the reservoir are based on the stimulated reservoir volume, and wherein the generated linear flow volume graph is generated based on a slope and intercept from a generated normalized pressure graph that includes normalized pressure values for a plurality of timestamps using time, the pressure data, and the cumulative production data; and performing at least one field operation in response to the identified end of the linear flow from the generated linear flow volume graph.
 19. The method of claim 18, further comprising identifying a type of boundary after the linear flow. 